Transcript Lecture 3
INC 111 Basic Circuit Analysis Week 3 Nodal Analysis
Systematic Methods for Analyzing a Circuit •
Nodal Analysis
•
Mesh Analysis (Loop analysis)
Node
Node = Point that connected together on the same wire Example
10V 6K 4K
V 3 nodes
Nodal Analysis
Procedure 1. Count the number of nodes = N 2. Choose one of the nodes to be a reference node (0V) when there is no ground 3. Give the voltage for other nodes to be V1, V2, V3, … 4. Use Kirchoff’s current law on each node to form N-1 equations 5. Solve the equations to find V1, V2, V3, …
V1
Example
V2
5 Ω 2 Ω 1 Ω 3A
0V (reference)
2A
V1
2 Ω 5 Ω 1 Ω
V2
3A
0V (reference)
3 30
V
5 1 2
V
0 1
V
1 ( 2
V
1 5
V
2 2
V
2 ) 0 0 7
V
1 2
V
2 30
Equation 1
2A
V1
2 Ω 5 Ω 1 Ω
V2
3A
0V (reference)
V
(
V
2
V
1 2 5
V
1 )
V
2 1 5
V
2 0 2 10 0 0
V
1 6
V
2 10
Equation 2
2A
3A Solve the Equations
V1 V2
5 Ω 2 Ω 1 Ω 2A
V1 = 5 V V2 = 2.5V
Example -8A
V1
4 Ω -3A 3 Ω
V2
2 Ω 1 Ω 5 Ω
V3
-25A
0V
-8A
V1
4 Ω -3A 3 Ω
V2
2 Ω 1 Ω 5 Ω
V3
-25A
0V
8 96
V
1
V
4 3
V
1 3 3
V
3 3
V
1 36
V
2 3 4
V
1 0 4
V
2 0 7
V
1 4
V
2 3
V
3 132
Equation 1
-8A
V1
4 Ω -3A 3 Ω
V2
2 Ω 1 Ω 5 Ω
V3
-25A
0V
V
2
V
2 2 3
V
1 3
V
2
V
1 18 2
V
3 3 2
V
2
V
2 3
V
3 1 0 6
V
2 0 0 2
V
1 11
V
2 3
V
3 18
Equation 2
-8A
V1
4 Ω -3A 3 Ω
V2
2 Ω 1 Ω 5 Ω
V3
-25A
0V
V
3 10
V
V
2 2 3 10
V V
2 3
V
4 5
V
1 3 25 5
V
1
V
3 5 500 0 4
V
0 3 0 5
V
1 10
V
2 19
V
3 500
Equation 3
Solve the Equations 7
V
1 4
V
2 3
V
3 132 2
V
1 11
V
2 3
V
3 18 5
V
1 10
V
2 19
V
3 500
Cramer’s Rule (Optional) 7
V
1 4
V
2 3
V
3 132 2
V
1 11
V
2 3
V
3 18 5
V
1 10
V
2 19
V
3 500
V
1 132 18 500 7 2 5 11 10 4 11 10 4 3 19 3 3 19 3 780 816 0 .
956
V
2 7 2 5 7 2 5 132 18 500 4 11 10 3 3 19 3 3 8628 816 10 .
576 19 7
V
1 4
V
2 3
V
3 132 2
V
1 11
V
2 3
V
3 18 5
V
1 10
V
2 19
V
3 500
V
3 7 2 5 4 7 2 5 11 10 4 11 10 132 18 500 19 3 3 26220 32 .
132 816
Supernode
When there is a voltage source in the circuit, direct KCL cannot be used because we do not know the current in the voltage source.
We will use the idea of supernode.
Supernode is the method that combines 2 nodes together when using KCL. It will include the voltage source within the circle when using KCL.
Example -8A
V1
4 Ω -3A 3 Ω
V2
1 Ω 1V 5 Ω
V3
-25A
0V
-8A
V1
4 Ω -3A 3 Ω
V2
1 Ω 1V 5 Ω
V3
-25A
0V
8 96
V
1
V
3
V
4 1 3 3
V
3 3
V
36 1
V
2 3 4
V
1 0 4
V
2 0 7
V
1 4
V
2 3
V
3 132
Equation 1
-8A
V1
4 Ω -3A 3 Ω
V2
1 Ω 1V 5 Ω
V3 supernode
-25A
V
2 20
V
3 2
V
1 20
0V
3
V
1
V
3 4 180
V
1 15
V
25 3
V
3 5 15
V
1 0
V
1500 2 1 0 12
V
3 0 60
V
2 0 35
V
1 80
V
2 27
V
3 1680
V
2
V
3 1
Equation 3 Equation 2
7
V
1 4
V
2 3
V
3 132 35
V
1 80
V
2 27
V
3 1680
V
2
V
3 1
V1 = -4.952 V V2 = 14.333 V V3 = 13.333 V
3V
V1
Example
V2
5 Ω 2 Ω 1 Ω 2A
0V
V
1 3
V
2
V
1 5 2
V
2 0 1 0
V
2 13 6
Sanwa YX360TRF Multimeter
Dial
Sanwa YX360TRF Multimeter
Resistance Zero Adjust Range Selector
Resistance Measurement
Read this Range Select these ranges
Voltage Measurement
Read this Range Select these ranges
Current Measurement
Read this Range Select these ranges
Measure the Resistance of Ammeter and Voltmeter
Adjust a multimeter to measure volt and use another multimeter to measure its resistance.
Adjust a multimeter to measure amp and use another multimeter to measure its resistance.
Resistor Code
Standard Resistor Value
E12 -Standard
1R0 1R2 1R5 1R8 2R2 2R7 3R3 3R9 4R7 5R6 6R8 8R2 10R 12R 15R 18R 22R 27R 33R 39R 47R 56R 68R 82R 100R 120R 150R 180R 220R 270R 330R 390R 470R 560R 680R 820R 1K0 1K2 1K5 1K8 2K2 2K7 3K3 3K9 4K7 5K6 6K8 8K2 10K 12K 15K 18K 22K 27K 33K 39K 47K 56K 68K 82K 100K 120K 150K 180K 220K 270K 330K 390K 470K 560K 680K 820K 1M0 1M2 1M5 1M8 2M2 2M7 3M3 3M9 4M7 5M6 6M8 8M2 10M n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
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